Just for point of reference...I fished two farm ponds over the weekend. One was fenced off from the cattle while the other was not. Both were muddy, 2" visibility at best, and both ponds loaded with small CC. Overstocked, I suppose, with no feeding regiment or management for that matter. Point is, the ponds were muddied up from the cats constantly foraging for food that's not there. We caught one fish after another, sometimes two at the same time (fished with two poles until I could not keep up with the catch rates). The ponds were so full of hungry little fish that there's no way to clear the water up.
I think you are on the right track by fishing to determine what's in there. My fear would be a lot of BHC...I have no need for them unless kids fishing is all that the pond is for. Those little cats can be trapped, from what I have read, and tossed or relocated. Try live panfish/perch for bait, but make they are bigger than the largest bullhead could eat that you have already caught. Target larger cats or bass. If all you have is BHC then adding bass will help reduce the survival of BH YOY, but from what others have stated, turning a bull head pond around can take some patience combined with culling dedication.
How did the fish look? skinny, fat, big eyes, light/dark coloration? Did you take weights and lengths?
